Shortness coefficient of cyclically 4-edge-connected cubic graphs

Publikationstyp
Journal Article
Publikationsdatum
2020-02-07
Sprache
English
Author
Lo, On-Hei Solomon 
Schmidt, Jens M. orcid-logo
Van Cleemput, Nico 
Zamfirescu, Carol T. 
DOI
10.15480/882.3190
TORE-URI
http://hdl.handle.net/11420/7601
Enthalten in
The electronic journal of combinatorics 
Volume
27
Issue
1
Start Page
1
End Page
12
Article Number
P1.43
Citation
Electronic Journal of Combinatorics: 1 (27): P1.43, 1-14 (2020)
Publisher DOI
10.37236/8440
Scopus ID
2-s2.0-85079448712
Grünbaum and Malkevitch proved that the shortness coefficient of cyclically 4-edge-connected cubic planar graphs is at most76 77. Recently, this was improved to (Formula Presented) and the question was raised whether this can be strengthened to 42, a natural bound inferred from one of the Faulkner-Younger graphs. We prove that the shortness coefficient of cyclically 4-edge-connected cubic planar graphs is at most 37 38 and that we also get the same value for cyclically 4-edge-connected cubic graphs of genus g for any prescribed genus g ≥ 0. We also show that45 46 is an upper bound for the shortness coefficient of cyclically 4-edge-connected cubic graphs of genus g with face lengths bounded above by some constant larger than 22 for any prescribed g ≥ 0.
DDC Class
510: Mathematik
Publication version
publishedVersion
Lizenz
https://creativecommons.org/licenses/by-nd/4.0/
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